Problem: Simplify to lowest terms. $\dfrac{16}{56}$
There are several ways to tackle this problem. What is the greatest common factor (GCD) of 16 and 56? $16 = 2\cdot2\cdot2\cdot2$ $56 = 2\cdot2\cdot2\cdot7$ $\mbox{GCD}(16, 56) = 2\cdot2\cdot2 = 8$ $\dfrac{16}{56} = \dfrac{2 \cdot 8}{ 7\cdot 8}$ $\hphantom{\dfrac{16}{56}} = \dfrac{2}{7} \cdot \dfrac{8}{8}$ $\hphantom{\dfrac{16}{56}} = \dfrac{2}{7} \cdot 1$ $\hphantom{\dfrac{16}{56}} = \dfrac{2}{7}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{16}{56}= \dfrac{2\cdot8}{2\cdot28}= \dfrac{2\cdot 2\cdot4}{2\cdot 2\cdot14}= \dfrac{2\cdot 2\cdot 2\cdot2}{2\cdot 2\cdot 2\cdot7}= \dfrac{2}{7}$